Sinusitis: This condition is characterized by inflammation of the sinuses, often due to infection. The symptoms of facial swelling and pain, particularly around the nose and upper lip, along with cough, are classic for sinusitis. The cough can be a result of postnasal drip, which is common in sinus infections.

Dental Infection: Infections of the teeth or gums can cause facial pain and swelling, especially if the infection spreads to the surrounding tissues. A cough might not be a direct symptom but could be related to the overall discomfort or if the infection leads to a secondary issue like sinusitis.
Allergic Rhinitis: This condition involves an allergic reaction to airborne allergens, leading to nasal congestion, runny nose, and sinus pressure. These symptoms can cause facial pain and swelling, particularly around the nose and upper lip. Coughing can occur due to postnasal drip.
Viral Upper Respiratory Infection: Common colds or other viral infections can cause sinus pressure, facial pain, and cough. The facial swelling might be less pronounced but can occur due to sinus congestion.

Ludwig's Angina: Although rare, this is a severe infection of the tissues in the neck, which can cause significant swelling and pain. It's a medical emergency because it can lead to airway obstruction. A cough might be present, and while it's less likely, missing this diagnosis could be fatal.
Wegener's Granulomatosis (Granulomatosis with Polyangiitis): This is a rare autoimmune disorder that can cause inflammation of the blood vessels, leading to symptoms like sinusitis, cough, and facial pain. It's crucial to consider this diagnosis due to its potential severity and the need for specific treatment.
Cellulitis or Abscess: Bacterial infections of the skin and soft tissues can cause swelling, pain, and redness. While a cough might not be directly related, in severe cases, these infections can lead to systemic symptoms, including fever and malaise, which might indirectly cause a cough.

Sarcoidosis: This is a condition where inflammatory cells form lumps known as granulomas in various parts of the body, including the sinuses and lungs. It can cause facial swelling, sinus pressure, and cough, among other symptoms.
Relapsing Polychondritis: A rare autoimmune disorder that can cause cartilage inflammation, leading to symptoms like nose and ear pain, and potentially cough if the tracheal cartilages are involved.
Midline Destructive Granuloma: A rare condition that can cause destruction of the midline facial tissues, including the nose and sinuses, potentially leading to facial pain, swelling, and cough due to the involvement of the respiratory tract.